算数・数学教育における学習の所産に関する研究 : 自分の考えを表現する算数的/数学的活動の必然性について

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  • A Study about the Nature of "Product" in Mathematics Learning : Inevitability of Expressing the Learners' Ideas Within Their Mathematical Activities
  • サンスウ スウガク キョウイク ニ オケル ガクシュウ ノ ショサン ニ カンスル ケンキュウ ジブン ノ カンガエ オ ヒョウゲン スル サンスウテキ スウガクテキ カツドウ ノ ヒツゼンセイ ニ ツイテ

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Expressing the learners' ideas, or cultivating students' ability of representation, have been focused on as the important mathematical activities in these days. Some of such activities are Learning Playback (Nakamura, 1989), Balloon Method (Kameoka, 1990), Reflexive Writing Activity (Ninomiya, 2005(a)), and so on. These "explaining one's understanding" activities tend to be more focused on. In this paper, inevitability of such tendency is examined. From the basic idea of Hirabayashi (2001(a)), ecological viewpoint is adopted for both methodological and contextual examination. Through the outcomes of Uchida (1986) and Ninomiya (2005(a)), reflexive nature of thinking and representing is pointed out, and it is found that expressing the idea makes the learner think deeper. From such reflexive nature, the nature of "Product" is shown, as "knowing the achievement of what they have learnt". Within such vision, the theory of Meta-learning, by Bateson and Mellin-Olsen, and the theory of Implicit and Explicit Mathematics, by Chevallard are examined. From the viewpoint of learning activity, Meta-learning, or learning 2 in Bateson's term, may result the outcome of learning as "knowing the achievement of what they have learnt". On the other hand, From the viewpoint of mathematical knowledge, both implicit and explicit products should be aware of, for the ideal learning outcome, as "knowing the achievement of what they have learnt".

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